[6] Should the reader be quite fresh to the subject, he is recommended to draw out for himself,—merely roughly mark down,—the several dispositions of columns which have been spoken of; for by compelling him to consider them carefully, he will be better able to understand them, and have them distinctly impressed upon his memory. The annexed may serve as a specimen of such short-hand architectural notation, in asterisks. * * * * * * * * * * * * * * Peripteral Hexastyle, * * 12 intercolumns * * on sides. * * * * * * * * * * * * * * Besides the restriction as to general proportion of plan, namely, the fixed relationship between the length and the breadth of the building, proportion with regard to height was limited in a different way, and in such a manner that the character of increased richness and importance derived from a greater number of columns was attended, not indeed by decreased height, but by _decreased loftiness_, or proportional height, that is, height as measured by either breadth or length. Paradoxical as this may sound at first, nothing can be more clear when once explained. Discarding nicety of measurement, we will call a _tetrastyle_ portico about a square in height, that is, about as high as wide; but add four more columns, extend it from a tetrastyle to an octastyle, so that it becomes about a double square in breadth, or twice as wide again, and the inevitable consequence is, that it is then only half as high as wide; that is, as to proportion, only half as _lofty_ as it was before. The expression of _loftiness_, in which altitude greatly predominates over breadth, was quite beyond the reach of the Greek system. Their temples might be planted on lofty eminences, but the structures themselves never towered upwards. As far as it went, their system was perfect,—so complete indeed in itself as to be unfit for almost any other purposes than that for which it was expressly framed. If the Romans corrupted the Greek Orders, the Doric and Ionic, they developed and matured the Corinthian Order, and also worked out a freer and more complex and comprehensive system of Architecture. To say nothing of their introduction and application of those important elements of both construction and design, the arch and vault—which hardly belong to a mere treatise on the Orders—it is to the Romans that we are indebted for varieties and combinations of plan that will be sought for in vain among Grecian structures.